When the maximum ring of quotients of C ( X ) is uniformly complete
نویسنده
چکیده
A Tychonoff space X such that the maximum ring of quotients of C(X) is uniformly complete is called a uniform quotients space. It is shown that this condition is equivalent to the Dedekind– MacNeille completion of C(X) being a ring of quotients of C(X), in the sense of Utumi. A compact metric space is a uniform quotients space precisely when it has a dense set of isolated points. Extremally disconnected spaces and almost P -spaces are uniform quotients spaces. Also characterized are the compact spaces of dense constancies which are uniform quotients spaces. 2001 Elsevier Science B.V. All rights reserved. AMS classification: Primary 54H10; 06F25; 13B30, Secondary 54D35; 54G05
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